Recently, in the department of neuropsychiatry, an intelligence testing method has been proposed for knowing the degree of advancement of intelligence or diagnosing aging and dementia.
As for conventional techniques, tests for finding a decrease in the mentation of old people include a Hasegawa type dementia scale and an N-type mentation test. These tests judge whether or not a subject can correctly answer questions concerning orientation and impressibility.
On the other hand, according to what is experienced in picture drawing therapy, pictures drawn by many old people are characterized by loss of freedom and collapse of form. This suggests that a decrease in mentation can be surmised from pictures. However, pictures themselves contain so much information that quantitization is difficult. Therefore, development of a method of judgement was started in about 1987, which method, substituting the act of "marking points" which is the simplest form of drawing pictures, is based on the analysis of distribution or locus of points (references: "ANALYSIS OF POINTS"--PRELIMINARY STUDY, Mikio Hayashi and Toshikazu Hakamada, Kosei-Nenkin Hospital Annual Report Vol. 14 (1987), pp. 283-290; "ANALYSIS OF POINTS"--PRELIMINARY STUDY II, Mikio Hayashi, Makiko Tominaga and Syuniti Hakamada, Kosei-Nenkin Hospital Annual Report Vol. 15 (1988), pp. 317-323; "EARLY DETECTION OF DEMENTIA IN PICTURE THERAPY", Mikio Hayasi and Chitaru Tanaka, in CLINICAL PICTURE STUDY IV (1988), published by Kongo Publishing Co., Ltd., pp. 33-48, "ANALYSIS OF POINTS"--PRELIMINARY STUDY III, Mikio Hayashi and Chitaru Tanaka, Kosei Nenkin Hospital Annual Report Vol. 16 (1989), pp. 323-339). The principle of this "point analysing method" consists of instructing a subject to enter a plurality of points (I points) randomly and distributively in M (vertical).times.N (horizontal) quadratures and specifying the positions of the points by the coordinates of the quadratures in which they are entered.
As a precondition, let the horizontal direction of the quadratures be called the x direction and the vertical direction thereof the y direction. As the numbers adopted since the beginning of the development of the method, the number of columns (the number of quadratures in the x direction) M=12 and the number of rows (the number of quadratures in the y direction) N=20 and the number of entered points I=30. If the i-th entered point (i=1, 2, . . . , 3) is entered in a quadrature which is located at the a.sub.i -th position from the left and b.sub.i -th position from the top, the coordinates of said point are (a.sub.i, b.sub.i). In this case, a.sub.i and b.sub.i are integers which satisfy the relations 1.ltoreq.a.sub.i .ltoreq.12 and 1.ltoreq.b.sub.i .ltoreq.20.
Let {u.sub.i, v.sub.i)} be the progression of difference in the order sequence {(a.sub.i, b.sub.i)} of the coordinates of the 30 points. That is, EQU u.sub.i =a.sub.i+1 -a.sub.i EQU v.sub.i =b.sub.i+1 -b.sub.i
In this case, i=1, 2, . . . , 29.
As is clear from this definition, u.sub.i and v.sub.i are integers which satisfy the relations: EQU -11.ltoreq.u.sub.i .ltoreq.11, EQU -19.ltoreq.v.sub.i .ltoreq.19.
(1) First method: dispersion in distribution of points
Let m.sub.k be the number of points i whose x coordinates satisfy the relation a.sub.i =k, that is, which belong to the k-th column, and
let n.sub.t be the number of points i whose y coordinates satisfy the relation b.sub.i =t, that is, which belong to the t-th column.
Then D.sub.x and D.sub.y are found as follows. ##EQU1## Since I/M=5/2 and I/N=3/2 are the total number of marked points divided by the number of columns and by the number of rows, respectively, they are values which should be the average number of marked points in each column and each row in a large number of samples in which the points are marked truly at random. Therefore, D.sub.x and D.sub.y respectively represent the sums of deviations from the average values of the numbers of actually marked points in each column and each row. The coordinates (D.sub.x, D.sub.y) are specified and the lowering in mentation is judged from the positional relation to the origin or normal range (to be later described).
(2) Second method: Amount of movement of dispersion
Each of the progression of difference {(u.sub.i, v.sub.i)} represents the distances (the numbers of quadratures) in the row and column directions traveled from the i-th marked point to the i+1-th marked point, the sum of .vertline.u.sub.i .vertline. (i=1, 2, . . . , 29) and the sum of .vertline.v.sub.i .vertline. (i=1, 2, . . . , 29) represent the sizes of dispersions of marked points in each direction.
That is, ##EQU2## where S is called the amount of movement. In this example, S is compared with a preset reference value S.sub.o =7900 and if S is found greater than said reference value, the mentation is judged to be normal and if it is smaller than said reference value the mentation is judged to have been lowered.
(3) Third method: dispersion of movement (displacement)
Let .nu..sub.k be the number of points i which satisfy the displacement of marked points in the x direction, u.sub.i =k, that is, the number of occurrences of the displacement k in the x direction, and
let .lambda..sub.t be the number of points i which satisfy the displacement of marked points in the y direction, v.sub.i =t, that is, the number of occurrences of the displacement t in the y direction.
Then, T.sub.x and T.sub.y are found as follows: ##EQU3## The coordinates (T.sub.x, T.sub.y) specify points presented by the sample.
The meaning of T.sub.x, T.sub.y is as follows. The values which the representative value a.sub.i in the sequence {a.sub.i } can take are integers ranging from 1 to M=12. Then, u.sub.i can be values-(M-1), -(M-2)- . . . -1, 0, 1, . . . ,M-1. Therefore, when k.gtoreq.0, there are M.times.k ways in which u.sub.i =k, as shown in Table I.
TABLE 1 ______________________________________ a.sub.i 1 2 . . . M - k a.sub.i+1 k + 1 k + 2 . . . M ______________________________________
Similarly, when k&lt;0, there are M-.vertline.k.vertline. ways.
If each term in {ai} is independent, then the occurrences of all sets of a.sub.i and a.sub.i+1 which have M.times.M ways are of equal probability. It is seen from the above discussion that since there are M-.vertline.k.vertline. ways in which u.sub.i =k, the probability of u.sub.i =k is EQU f(x)=(M-.vertline.k.vertline.)/M.sup.2 (the second term in the T.sub.x equation)
Since {a.sub.i } consists of I-1=29 terms, the average value of the frequency of occurrence of i such that u.sub.i =k is 29.times.f(x) if the marking of points is at random. (This applies also to the sequence {b.sub.i }, and the T.sub.y equation holds.)
After all, it will be understood that T.sub.x and T.sub.y are quantities indicating how much the frequency of occurrence of displacement in the x and y directions deviates from the frequency of occurrence which obeys this probability distribution. However, it should be noted that in a strict sense, the independence of a.sub.i and a.sub.i+1 does not hold. The reason is that two points cannot occupy the same quadrature at the same time. However, since T.sub.x and T.sub.y are considered to be a single function which substantially formularizes the dispersion of displacement (movement), it is not necessary to treat f(K) as probability distribution in a strict sense. In brief, it s important that T.sub.x and T.sub.y form a function such that there is a difference between a group of patients and a control group (a group of subjects to be considered normal).
(4) Dispersion index
(D.sub.x, D.sub.y) and (T.sub.x, T.sub.y) represent "dispersion of distribution of points" and "dispersion of movement of points" of a sample, respectively. The linear combination of these quantities is referred to as "dispersion index". That is, the "dispersion index of coefficient .mu.": (V.sub.x, V.sub.y).sub..mu. is defined by the following formula. EQU (V.sub.x, V.sub.y).sub..mu. =(D.sub.x, D.sub.y)+.mu.(T.sub.x, T.sub.y)
where .mu.&gt;0.
To evaluate the test results, the calculated values for the respective subjects are plotted on a graph. Similar tests are conducted in advance on healthy person to find the range of healthy person, it being surmised that the further the calculated values are deviated from this range drawn on the same graph, the greater the degree of dementia. In this case, the normal ranges of the calculated values (D.sub.x, D.sub.y) according to the first method and the calculated values (T.sub.x, T.sub.y) according to the third method are circles having center coordinates substantially determined by probability calculations, while in the second method judged by the product S of the x-coordinate X and y-coordinate, the normal range is a hyperbola (only in the first quadrant) expressed by xy=S.sub.o (where S.sub.o is a constant, which is 7900 in the above example), and it is judged that the upper right of the hyperbola is normal and the lower left means that there is a decrease in mentation.
In conventional tests, a subject is instructed to mark points on a test paper sheet. Although the coordinates of points can be found from the collected paper sheet, the order in which the points are entered cannot be found; therefore, the numbers of points in the columns and rows are visually counted, and from the counted results, calculations according to the first method are made by writing or by using a computer. In addition, the second and third methods requiring information on the order of marking the points have been experimentally verified by telling a subject to enter numerals rather than points.